STOKESIAN DYNAMICS 113 calculations are by no means exact for all particle-particle separations, but they do give some indication of the importance of three-body and higher order effects (Beenakker & Mazur 1983, 1984, Beenakker 1984). addition to many-body interactions, lubrication forces play a predominant role in determining suspension structure and behavior at high concentrations. Lubrication forces, as the name implies, result from the thin layer of viscous fluid that separates the surfaces of nearly touching particles; one of the effects of these forces is that the relative motion of particles tends to zero as the particle surfaces approach one another. Thus, to accurately model the behavior of particles in suspension, both of these important hydrodynamic effects need to be addressed. Another aspect of the hydrodynamic interactions that causes considerable difficulty (not to mention confusion) is their long-range character. The fluid velocity disturbance caused by a particle on which a net external force acts decays as I/r, where r is the distance from the particle. A large collection of such forced particles, i.e. an infinite sedimenting suspension, results in a severely nonconvergent sum of interactions; the velocity of a test particle diverges as R 2, where R is the size of the system. If the particles are fixed in space, as in a porous medium, rather than having a prescribed force, the long-range interactions actually change the fundamental character of the velocity disturbance caused by a particle, resulting in a screening of hydrodynamic interactions (

A general method for computing the hydrodynamic interactions among N suspended particles, under the condition of vanishingly small particle Reynolds number, is presented. The method accounts for both near-field lubrication effects and the dominant many-body interactions. The many-body hydrodynamic interactions reproduce the screening characteristic of porous media and the 'effective viscosity ' of free suspensions. The method is accurate and computationally efficient, permitting the dynamic simulation of arbitrarily configured many-particle systems. The hydrodynamic interactions calculated are shown to agree well with available exact calculations for small numbers of particles and to reproduce slender-body theory for linear chains of particles. The method can be used to determine static (i.e. configuration specific) and dynamic properties of suspended particles that interact through both hydrodynamic and non-hydrodynamic forces, where the latter may be any type of Brownian, colloidal, interparticle or external force. The method is also readily extended to dynamically simulate both unbounded and bounded suspensions.

The newly developed simulation method known as Stokesian dynamics is used to investigate the rheological behaviour of concentrated suspensions. Both the detailed microstructure (e.g. pair-distribution function) and the macroscopic properties are determined for a suspension of identical rigid spherical particles in a simple shear flow. The suspended particles interact through both hydrodynamic and non-hydrodynamic forces. For suspensions with purely hydrodynamic forces, the increase in the suspension viscosity with volume fraction ϕ is shown to be caused by particle clustering. The cluster formation results from the lubrication forces, and the simulations of a monolayer of spheres show a scaling law for the cluster size: lc ∼ [1 − (ϕ/ϕm)½]−1, where ϕm is the maximum volume fraction that can shear homogeneously. The simulation results suggest that the suspension viscosity becomes infinite at the percolation-like threshold ϕm owing to the formation of an infinite cluster. The predicted simulation viscosities are in very good agreement with experiment. A suspension with short-range repulsive interparticle forces is also studied, and is seen to have a non-Newtonian rheology. Normal-stress differences arise owing to the anisotropic local structure created by the interparticle forces. The repulsive forces also reduce particle clustering, and as a result the suspension is shear-thickening.

No abstract

The viscosity of a suspension of spherical Brownian particles is determined by Stokesian dynamics as a function of the Péclet number. Several new aspects concerning the theoretical derivation of the direct contribution of the Brownian motion to the bulk stress are given, along with the results obtained from a simulation of a monolayer. The simulations reproduce the experimental behavior generally observed in dense suspensions, and an explanation of this behavior is given by observing the evolution of the different contributions to the viscosity with shear rate. The shear thinning at low Péclet numbers is due to the disappearance of the direct Brownian contribution to the viscosity; the deformation of the equilibrium microstructure is, however, small. By contrast, at very high Péclet numbers the suspension shear thickens due to the formation of large clusters.

The non-equilibrium behaviour of concentrated colloidal dispersions is studied by Stokesian Dynamics, a general molecular-dynamics-like technique for simulating particles suspended in a viscous fluid. The simulations are of a suspension of monodisperse Brownian hard spheres in simple shear flow as a function of the Peclet number, Pe, which measures the relative importance of shear and Brownian forces. Three clearly defined regions of behaviour are revealed. There is first a Brownianmotion-dominated regime ( P e < 1) where departures from equilibrium in structure and diffusion are small, but the suspension viscosity shear thins dramatically. When the Brownian and hydrodynamic forces balance (Pe w lo), the dispersion forms a new 'phase' with the particles aligned in 'strings' along the flow direction and the strings are arranged hexagonally. This flow-induced ordering persists over a range of P e and, while the structure and diffusivity now vary considerably, the rheology remains unchanged. Finally, there is a hydrodynamically dominated regime (Pe > 200) with a dramatic change in the long-time self-diffusivity and the rheology. Here, as the Pklet number increases the suspension shear thickens owing to the formation of large clusters. The simulation results are shown to agree well with experiment.

A general method is presented for simulating the dynamical behavior of a suspension of particles which interact through both hydrodynamic and nonhydrodynamic forces. In the molecular-dynamics-like simulation there are two different procedures for computing the interactions among particles: a pairwise additivity of forces and a pairwise additivity of velocities. The pairwise additivity of forces is the preferred method as it preserves the hydrodynamic lubrication forces which prevent particles from overlapping. The two methods are compared in a simulation of a monolayer of identical rigid non-Brownian spherical particles in a simple shear flow. Periodic boundary conditions are used to model an infinite suspension. Both methods predict the presence of a shear induced anisotropic local structure whose form and strength depend on the concentration of particles, the nonhydrodynamic forces, and the shear rate. Increasing the particle concentration up to near the maximum fraction that can still flow results in a transition to a layered structure in which planes of particles slide relative to one another. The anisotropic local structure and transition to a layered structure predict a non-Newtonian suspension rheology.

A magnetoactive elastomer made of micronic carbonyl iron particles, structured in elongated clusters and embedded in a silicon elastomer matrix is studied under traction both in static and dynamic modes. The application of a magnetic field of 120 kA/m induces a change in elastic moduli of about 0.6 MPa at strains of 4 to 5%. Still higher changes (4 MPa) are observed in dynamic storage modulus at low strains (10-4 to 10-3). The shape of the stress-strain curves are explained by taking into account the existence of a fiber like structure.